Geometric discretization of the Koenigs nets

Details Geometric discretization of the Koenigs nets Geometric discretization of the Koenigs nets

2002-03-07

arxiv.org/abs/nlin/0203011v2

J. Math. Phys. 44 (2003) 2234-2249

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, 2 figures; some spelling and typing errors corrected

Scientific paper

We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs lattice and we show permutability of superpositions of such transformations, thus proving integrability of the Koenigs lattice. We also investigate the geometry of the discrete Koenigs transformation. In particular we characterize the Koenigs transformation in terms of an involution determined by a congruence conjugate to the lattice.

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